Question

Find the volume of a pyramid with a square base, where the perimeter of the base is 19.1\text{ ft}19.1 ft and the height of the pyramid is 15.9\text{ ft}15.9 ft. Round your answer to the nearest tenth of a cubic foot.

Answer 1

The volume of the pyramid is 120.8 ft³

Explanation:

To find the volume of a square-based pyramid, we will follow the steps below:

write down the formula for finding the volume of a pyramid

v =A(h/3)

where v is the volume , A is the area and h is the height

From the question given perimeter of the base = 19.1 ft

since the base is a square, then;

perimeter = 4l = 19.1

4l = 19.1

Divide both-side of the equation by 4

4l/4 = 19.1/4

l = 4.775 ft

Area = l² = 4.775² ≈ 22.8 ft

Also, from the question height = 15.9 ft

v = A(h/3)

v = 22.8 (15.9/3)

v= 22.8×5.3

v=120.84

v≈120.8 ft³ to the nearest tenth of a cubic foot

The volume of the pyramid is 120.8 ft³